Supersymmetry And Electron-hole Excitation in Semiconductor At Finite Temperature

The fermionic and bosonic electron-hole low lying excitations in a semiconductor are analyzed at finite temperature in a unified way following Nambu's quasi-supersymmetric approach for the BCS model of superconductivity. The effective lagrangian for the fermionic modes and for the bosonic low lying collective excitations in the semiconductor is no longer supersymmetric in a conventional finite temperature treatment. However the bosonic excitations don't couple directly to the heat bath and as a result, quasisupersymmetry is restored to the effective lagrangian when a redefinition of the coupling constant associated with the collective excitations is performed. Our result shows that although the mass and coupling parameters are now temperature dependent, the fermion and boson excited states pair together and can still be transmuted into one another.